THE TRANSPORT A TION OF GASES 177
Pa, Tz, dz = corresponding values for the final conditions of the gas as it leaves the compressor.
7 = ratio of specific heats of gas, taken as 1.41.
A = czyro - i = (p2/pi)c^* - i = (WP!)0-289 - i.
8 = specific gravity of gas at inlet conditions, referred to that of "free air"
as unity.
/ quantity of inlet gas, cubic feet per second. 6h = hydraulic efficiency, referred to adiabatic compression. H = the theoretical (or total) head, or height against which the gas is raised.
feet, including all hydraulic losses. N revolutions per minute.
Total Pressure Rise.The fundamental equation giving the value of H is 1 as that for Hb (see " Centrifugal Pumps," p. 115). For single-stage compn
- (-)'
W
4,631pry
90deg. (no inlet guide vanes) and 60 90deg. (radial discharge). A ing pi = 14.7, Ti = 520, T = 1.41, eh = 0.72, and substituting, p2 = 14. (w0V4,300,000)]3-44. For small pressure rise, with de = 90deg., p2 - Pi = O.OC,
ehUa*S[l + (Va/Ua) COS 6J.
Fluid input horsepower is the horsepower applied to the gas and is independent of the actual pressure rise obtained. Fluid input horsepower = QdiH/55Q. For de = 90 deg., this becomes 0.00000432 Qsua*[l + (va/Ua) X cos bj.
Theoretical Horsepower. This is the horsepower necessary to compress (and deliver) Q cu. ft. of gas per second from p\ to p2.
Theoretical horsepower = 0.901Qpi(p2/pi)°"286 1; or, for small pressure rise = 0.2618Qpe, where pe = p2 pi. This formula may also be used for higher pressures if pi = 14.7 Ib. per square inch and pe (=50.6A) is regarded as the mean effective pressure for adiabatic compression from p\ to p2. Table 13 gives values of the mean effective pressure pe against values of p2 Pi for the usual case of pi 14.7.
TABLE 13
(P2 14.7), Ib. per square inch ............. 5 10 15 20 25 30 35 40 45 50
Pe, Ib. per square inch ...................... 4.5 8.2 11.4 14.3 16.9 19.3 21.5 23.5 25.4 27.2
Table 14 gives the theoretical horsepower necessary to compress adiabatically (and deliver) 100 cu. ft. of air per minute from 14.7 Ib. absolute to various gage pressures.
TABLE 14
Final gage pressure, Ib. per square inch 5 10 15 20 25 30 35 40 45 50 Theoretical horsepower per 100 cu. ft.. . . 1.95 3.58 4.99 6.25 7.37 8.39 9.35 10.23 11.06 11.84
Hydraulic Losses. The hydraulic losses are the losses in pressure caused by the gas friction and by the sudden changes in the gas velocity or direction of flow. On the basis of D. W. Taylor's experiments on the flow of air in pipes, the pressure drop in the suction and in the discharge pipes (pounds per square inch) = L fe2s/400r OOOD, where I is the length of pipe, feet, v the velocity of gas, feet per second, s the specific gravity of gas referred to free air (0.0764) as unity, and D the diameter of pipe, inches. For pipes of first-class workmanship and in very best condition, this loss may be reduced by about 20 per cent. The same care to have smooth pipe walls and to avoid too short bends should be taken with gases as with liquids.
Hydraulic Efficiency. The hydraulic efficiency is the ratio of the theoretical horsepower to the fluid input horsepower, or eh = l84.8ATi/H. For de = 90°, _ _5,955AT, ___ A] = __ 60,600(p2 - pO _
~ ' ' ** ~
Ua*[l +(VaZ/Ua) COS j
for small pressure rise, with de = 90 deg.
12